Rewrite as a simplified fraction. ${0.8\overline{70} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 870.707...\\ 10x &= 8.707...\end{align*}}$ Subtracting the two equations, we have: ${990x = 862}$ ${x = \dfrac{862}{990}} $ ${x = \dfrac{431}{495}} $